A353802 Multiplicative with a(p^e) = sigma(sigma(p^e)).

1, 4, 7, 8, 12, 28, 15, 24, 14, 48, 28, 56, 24, 60, 84, 32, 39, 56, 42, 96, 105, 112, 60, 168, 32, 96, 90, 120, 72, 336, 63, 104, 196, 156, 180, 112, 60, 168, 168, 288, 96, 420, 84, 224, 168, 240, 124, 224, 80, 128, 273, 192, 120, 360, 336, 360, 294, 288, 168, 672, 96, 252, 210, 128, 288, 784, 126, 312, 420, 720

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A051027, A353803, A353804, A353805, A353806.

Cf. also A336547, A336548, A353752.

Programs

PARI

A051027(n) = sigma(sigma(n));
A353802(n) = { my(f = factor(n)); prod(k=1, #f~, A051027(f[k, 1]^f[k, 2])); };

Formula

a(n) = Product_{p^e||n} sigma(sigma(p^e)), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

a(n) = A051027(n) + A353803(n).

a(n) = A353804(n) * A353806(n).